Internal Resonance Responses of Rectangular Cross-Ply Composite Plates with Graphene Skins

Abstract

This paper presents an investigation on the nonlinear dynamic behavior of three-phase rectangular composite plates made of cross-ply macro fiber composites (MFC) in the polymer with graphene (GP) skins, which are uniformly dispersed at the top and bottom surfaces of the plates. According to the mixture rules for multi-components of composite materials, the constitutive laws for MFC-GP composite materials can be obtained. A simply-supported rectangular plate model subjected to a transversal excitation in thermal environments is considered. The governing equations are formulated by using the first-order shear deformation theory, von Kármán geometrical kinematics and Hamilton’s principle. The Galerkin approach is used to discretize the governing equations for analysis. The vibration frequencies of MFC-GP composite plates with different modes are presented and the case of 1:2 internal resonance is selected to be investigated here. Three different coupled forms (i.e. uncoupled, weakly coupled and strongly coupled cases) of two vibration modes are presented. In addition, the influences of various parameters, including volume fraction of graphene, applied voltage, temperature effect and external excitation, on the nonlinear dynamic characteristics of MFC-GP composite plates are also examined.